# ABSOLUTE VALUE There are several ways to look at the absolute ABSOLUTE VALUE

There are several ways to look at the absolute value concept. One way is to consider the absolute value as the distance from the center of the number line to a given point. The center of the number line is the number zero . Since distance is always positive, we report the distance from zero to any point as a positive number. When asked what is the distance from Chicago to St.

Louis, you don't hear people say several hundred negative miles, do you? So distance numbers are positive numbers .

For example,

How "far" is it from 0 to the number 15? Answer: 15 units

-------------------0 --------------15

How "far" is it from 0 to the number -15? Answer: 15 units

15 --------------0------------------

Using the absolute value notation:

This leads into another way of looking at absolute values.

The absolute value is a function.

You put a number into it, and the number pops out positive .

If x is a negative number, change the sign of x and write the result.

If x is a positive number, don't change its sign. Write it as it is.

Change the sign of -15 and write the result: 15.

There is no need to change the sign. Just write the number 15.

The way we write "x is a negative number" is like this : x < 0.

"x is positive" is written as x > 0. If we include zero here, we write x > 0.

Hence, we can write the absolute value function like this:

It still works the same way as before, if x is a negative number, change its sign. Don't change the sign if x is positive.